Cook fettuccine. Meanwhile, in nonstick saucepan, heat 1 inch water to boiling over med-high heat. Add broccoli; heat to boiling. Reduce heat to med, cook 3 minutes or until broccoli is tender crisp. Drain and transfer to bowl and keep warm.
In same pan, heat oil over med. heat; add onion and garlic and cook until golden. In medium bowl whisk milk, chicken broth, flour, salt, pepper until blended; stir into saucepan and cook until mixture thickens and boils. Stir in Parmesan cheese. To serve, drain fettucine, toss fettucine and broccoli with sauce.